Let $f(x) = \dfrac{2-3x}{5-2x}$. For what value of $a$ is $f(a) = 3$?
I will assume you mean:
f(x) = (2-3x)/(5-2x) and you want to know the value of a so that
f(a) = 36
so (2-3a)/(5-2a) = 36
2 - 3a = 180 - 72a
69a = 178
a = 178/69
check my answer on your calculator by evaluating
f(178/69)
This is a aops problem which is why there are dollar signs (they signify latex)
So dont answer this problem to help a cheater. (reiny was wrong btw because you are solving for a value of a that gives f(a) = 3
To find the value of $a$ when $f(a) = 3$, we can substitute $3$ for $f(a)$ in the equation and solve for $a$.
We start by writing the equation $f(a) = 3$ as:
$$\frac{2-3a}{5-2a} = 3$$
Next, we can cross-multiply to eliminate the denominators:
$$(2-3a) \cdot 1 = 3 \cdot (5-2a)$$
Expanding both sides of the equation gives:
$$2 - 3a = 15 - 6a$$
Now, let's isolate the variable $a$ on one side of the equation. We can do this by adding $6a$ to both sides:
$$2 + 3a = 15$$
Next, subtracting $2$ from both sides gives:
$$3a = 13$$
Finally, dividing both sides by $3$ gives:
$$a = \frac{13}{3}$$
Therefore, the value of $a$ when $f(a) = 3$ is $\frac{13}{3}$.